Interpolation and Approximation with Splines and fractals
"A very valuable addition to the existing literature on the subject and the exposition takes the reader to very recent topics as Besov or Triebel-Lizorkin spaces, as well as their use in the theory of splines and fractals. Highly recommended for students or researchers working in applied fields who need to refresh their tools with current ones."--Libertas Mathematica "A useful book, well-written, and covering interesting areas of research in numerical analysis...A comprehensive volume. It is sufficiently introductory to be well readable for the non-expert while at the same time giving many interesting and useful results for the connaisseur."--Zentralblatt Math "There are several attractive features: historical footnotes sprinkled throughout the book, lots of beautifully designed figures, many well-chosen and easy-to-follow examples, and suggested student projects. The author does a great job in making available to students a set of fundamental topics at the crossroads of numerical analysis, functional analysis, fractals, and numerical harmonic analysis." -- Palle E. T. Jorgensen, MathSciNet
This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. Les mer
1723,-
Innbundet
Utsolgt
This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. This synthesis will complement currently required courses dealing with these topics and expose the prospective reader to some new and deep relationships. In addition to providing a classical introduction to the main issues involving approximation and
interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties. This also includes
the new burgeoning theory of superfractals and superfractal functions. The theory of splines is well-established but the relationship to fractal functions is novel. Throughout the book, connections between these two apparently different areas will be exposed and presented. In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling. Numerous examples, figures, and exercises accompany the
material.
interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties. This also includes
the new burgeoning theory of superfractals and superfractal functions. The theory of splines is well-established but the relationship to fractal functions is novel. Throughout the book, connections between these two apparently different areas will be exposed and presented. In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling. Numerous examples, figures, and exercises accompany the
material.
Detaljer
- Forlag
- Oxford University Press Inc
- Innbinding
- Innbundet
- Språk
- Engelsk
- ISBN
- 9780195336542
- Utgivelsesår
- 2010
- Format
- 24 x 16 cm
Anmeldelser
"A very valuable addition to the existing literature on the subject and the exposition takes the reader to very recent topics as Besov or Triebel-Lizorkin spaces, as well as their use in the theory of splines and fractals. Highly recommended for students or researchers working in applied fields who need to refresh their tools with current ones."--Libertas Mathematica "A useful book, well-written, and covering interesting areas of research in numerical analysis...A comprehensive volume. It is sufficiently introductory to be well readable for the non-expert while at the same time giving many interesting and useful results for the connaisseur."--Zentralblatt Math "There are several attractive features: historical footnotes sprinkled throughout the book, lots of beautifully designed figures, many well-chosen and easy-to-follow examples, and suggested student projects. The author does a great job in making available to students a set of fundamental topics at the crossroads of numerical analysis, functional analysis, fractals, and numerical harmonic analysis." -- Palle E. T. Jorgensen, MathSciNet